Finite categories and regular languages
Finite closed coverings of compact quantum spaces
We consider the poset of all non-empty finite subsets of the set of natural numbers, use the poset structure to topologise it with the Alexandrov topology, and call the thus obtained topological space the universal partition space. Then we show that it is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this partition space. In technical terms, we prove that the category of finitely supported...
Finite commutative monoids of open maps
Finite dimensional algebras and highest weight categories.
Finite objects and extensional relations
Finite presentation and purity in categories σ[M]
For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcategory of Mod-R containing M. If σ[M] is locally finitely presented the notions of purity and pure injectivity are defined in σ[M]. In this paper the relationship between these notions and the corresponding notions defined in Mod-R is investigated, and the connection between the resulting Ziegler spectra is discussed. An example is given of an M such that σ[M] does not contain any non-zero finitely presented...
Finite sets and symmetric simplicial sets.
Finitely generated almost universal varieties of -lattices
A concrete category is (algebraically) universal if any category of algebras has a full embedding into , and is almost universal if there is a class of -objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of -lattices which are almost universal.
Finitely generated almost universal varieties of 0-lattices.
Finitely generated Ext algebras.
Finitely generated universal varieties of distributive double -algebras
Finitely presentable morphisms in exact sequences.
Finitely silting comodules in quasi-finite comodule category
We introduce the notions of silting comodules and finitely silting comodules in quasi-finite category, and study some properties of them. We investigate the torsion pair and dualities which are related to finitely silting comodules, and give the equivalences among silting comodules, finitely silting comodules, tilting comodules and finitely tilting comodules.
Finiteness of a non-abelian tensor product of groups.
Finiteness of the strong global dimension of radical square zero algebras
The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density...
Finiteness Theorems for Deformations of Complexes
We consider deformations of bounded complexes of modules for a profinite group over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex to be represented by a complex of -modules that is strictly perfect over the associated versal deformation ring.
Finite-to-finite universal varieties of distributive double -algebras
Finitistic dimension and restricted injective dimension
We study the relations between finitistic dimensions and restricted injective dimensions. Let be a ring and a left -module with . If is selforthogonal, then we show that . Moreover, if is a left noetherian ring and is a finitely generated left -module with finite injective dimension, then . Also we show by an example that the restricted injective dimensions of a module may be strictly smaller than the Gorenstein injective dimension.
Firm reflections generated by complete metric spaces
Fittings's Invariants and a Theorem of Grauert.